Q4 of 23 Page 1

Solve any two sub-question:

If P(-2,4), Q(4,8), R(10, 5) and S(4, 1) are the vertices of a quadrilateral, show that it is a parallelogram.

To prove: PQRS is a parallelogram.

The quadrilateral is a parallelogram if opposite sides of quadrilateral are equal in length and parallel to each other


Consider PS and QR as opposite sides of quadrilateral


And PQ and RS as opposite sides of quadrilateral



Checking for PS and QR




Slope of PS = Slope of QR…(i)


Therefore, PS parallel to QR


Length of PS using distance formula



Length of QR



Length of PS = Length of QR…(ii)


Checking for PQ and RS




Slope of PQ = Slope of RS…(iii)


Therefore, PQ parallel to RS


Length of PQ using distance formula



Length of RS



Length of PQ = Length of RS…(iv)


Using equations (i),(ii),(iii) and (iv) we conclude that quadrilateral PQRS is a parallelogram


Hence proved


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